"Statistics is the logic of measurement, and all sciences require measurement." -- (S. M. Stigler, 1941 - )

Math History Tidbit:

Numbers have interesting historical backgrounds, and there are many interesting stories behind just about any counting number. Here are just a few very brief tidbits relating to numbers. (Some research will yield many interesting stories.)

8. Like most other single digit numbers, 8 has religious and mystical associations, but the ancients considered it interesting for purely mathematical reasons. It is closely associated with music, with 8 note in an octave. The Greeks discovered that every odd number greater than 1, when squared, results in a multiple of 8, plus 1. They also discovered that squares of odd numbers greater than 1 differed from each other by a multiple of 8.

9. The number 9 has been associated with both negative and positive things. The Chinese, Mongols, and Turkic peoples have been very fond of 9. On the other hand, some Christian writings associate it with pain and sadness; for example, the Ninth Psalm contains a prediction of the Antichrist. From a purely mathematical standpoint, it is the only square number that is the sum of two consecutive cubes. (13 + 23 = 9), and a number can be evenly divided by 9 only if its digits add up to a multiple of 9.


Herkimer's Corner

Why does Herkimer think that lions are very religious?

Answer: Because they prey a lot.

Herky's friends:

LAUREL N. HARDEE..she was a great fan of a comedy team from years ago.

PHIL TRATION...he sold water purifiers.


Reading: Section 10.1, pages 506-512.

Optional: Cartoon Guide to Statistics, pages 114-123...Good discussion of confidence intervals.

Exercises: 10.1, 10.2, 10.3, 10.4 (page 512)

Items for reflection:

You are working in Section 10.1.

Here's the basic idea: Suppose you take a randomsample of size 200 from a population with an unknown mean m, and aknown standarddeviation s = 1.34. The Central Limit Theorem tells us that thestandard deviation of the collection of means from all samples ofsize 10 is s/sqrt(200) = 1.34/sqrt(200) = 0.0948. Remember now... wedon't know the population mean. But, we can, within limits ofprobability, come up with some information about it. Suppose thatthe mean of the sample we took is 23.28. We will use the statistics23.28 to construct a 95% confidenceinterval for the unknown parameterm. Thisinterval has the form

estimate plus/minus 1.96( s /sqrt(N))

In the example provided, the 95% confidenceinterval is

23.28 plus/minus 1.96(0.0948) = 23.28plus/minus 0.19 = [23.09,23.47].

The margin oferror is plus/minus 0.19. This allows usto form an interval centered around our estimate (23.28). If we tookother samples of size 10, we could, using the sample means, constructother 95% confidence intervals. In a nutshell, 95% of the intervalsconstructed in this manner will contain the population parameter. Based on the one sample we examined, it is reasonable to assume thatthe population mean (a parameter) is between 23.09 and 23.47.





The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)

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